Mathematics

Problem

Consider the improper integral

\displaystyle \int_{0}^{\infty} \frac{x}{e^{x}-1}\,dx

. Which of the following statements about its convergence is correct? a) It diverges at both limits

x=0

and

x=\infty

. b) It converges over the entire interval

[0,\infty)

. c) It diverges only at the lower limit

x=0

. d) It diverges only at the upper limit

x=\infty